Phonons are the quantized vibrations of atoms in a dense material (solid or liquid). Several vibrational waves with different phases and amplitudes can be superposed to form a wavepacket which probability of existence is localized in space and time. This wavepacket is also called phonon and is seen as a quasi-particle. Monte-Carlo simulations of heat transport are based on the modelisation of the motion of quasi-particle phonons.

The Monte-Carlo code we have developped focuses on the semi-ballistic regime at low temperature, where the geometry and roughness of the system play a central role. This regime lies in between the coherent transport regime, where phonons are described by elastic waves, and the high temperature regime, where phonon-phonon interactions dominate. The semi-ballistic regime is today easily accessible by using liquid helium (4.2K) and nanolithography.

We show that the edge roughness of nanoribbons is an efficient way to cut-off high frequency phonons. The rough nanoribbon acts as a low-pass frequency filter. The cut-off frequency is determined by the roughness, almost independently of the geometry of the nanoribbon. However, the efficiency of the filtering effect is very sensitive to the geometry as the attenuation of the high frequencies increases when the length over width ratio increases.

Boundary scattering at the geometrical edges of a nanowire

Energy transmission in a nanoribbon for different edge roughnesses

Further information: Ramiere A., Volz S. & Amrit J. Geometrical tuning of thermal phonon spectrum in nanoribbons. J. Phys. D: Appl. Phys. **49**, 115306 (2016)